GF ZZ -- make a finite field of a given order

GF ZZ -- make a finite field of a given order

Synopsis:

Function: GF -- make a finite field

Input:

an instance of class ZZ.

Output:

an instance of class GaloisField.

Optional arguments :

GF(..., PrimitiveElement) -- specify a primitive element

GF(..., Variable) -- specify a name for the generator of a Galois field

GF(q) -- make a Galois field with q elements, where q is a power of a prime.

i1 : k = GF(8)



o1 = k



o1 : GaloisField

i2 : x = k_0



o2 = $a



o2 : k

i3 : x+x^2



       4

o3 = $a



o3 : k

Code:

     -- ../../../Macaulay2/m2/galois.m2:66-70
     GF(ZZ) := GaloisField => options -> (q) -> (
          factors := factor q;
          if #factors =!= 1 or factors#0#0 === -1
          then error "expected a power of a prime";
          GF(factors#0#0,factors#0#1,options))